Following a week of uncertainty in which Alastair Cook raised the suggestion he may not continue as England’s captain, the batsman confirmed what everybody listening to him felt, that he wished to continue in the job – indeed he was “desperate” to do so.

Moreover, he believed it would be wrong to change leadership with the World Cup just over a year away. It was a welcome positive assertion on the day England finally broke their losing habit.

After the 57-run win at the Waca, Cook was as relaxed as he was taut days earlier when England were easily beaten at Sydney, two days after throwing away a winning position in Brisbane.

The difference, Cook said, was speaking with his team-mates, who have publicly backed him this week, and that made him realise he wants to stay on. Before the match, he said: “I’m lucky enough to do this job. I’m desperate to carry on now.”

Afterwards, he added: “I spoke what I was feeling at the time [in Sydney] which probably you shouldn’t do. But we can move on. When you win a game of cricket, everyone thinks you’re a good captain. When you lose, everyone thinks you’re not.

“You do learn all the time and three years is quite a long time to do it. It would be wrong to change so close to the World Cup and if I’m given the opportunity to continue, obviously I would like to.

“In the last four or five days I have done quite a lot of talking to some of the guys. Sometimes you do need a bit of reassurance when you’ve lost a lot of games on a tour. When you chat to some guys you trust and you respect what they’re thinking, it gives you the confidence.”

On finally managing to beat the Aussies for the first time on this tour, Cook added: “It feels pretty good, to be honest with you. It has been a long time coming but the thought of losing 10-0 was a cross to bear. We did a lot of things very well today.”

One man in particular to have done things well was all-rounder Ben Stokes, who had been targeted by the Australians in the dramatic one-wicket defeat in Brisbane a week ago, when Australia chased down 300.

The Durham man this time claimed three important late wickets, including Australia’s Gabba hero James Faulkner.

“The thing I like about Stokesy is he had a tough last over in Brisbane when he didn’t get it right but there was no stopping him today wanting to bowl in those last 10 [overs],” Cook said. “He improved from Brisbane. If he keeps on that learning curve and dusts himself off when it doesn’t go well he’s going to be a hell of a cricketer.”

Wicketkeeper-batsman Jos Buttler’s impact was no less important as he crashed four sixes and six fours, before his fifth catch with the gloves completed victory.

“I’ve seen him do that with the bat a huge amount of times for Somerset,” Cook said. “He’ll be first to admit it took him a little bit of time to find his feet in international cricket but he’s growing all the time.

“The game is very different to the county game and what had impressed me is how he’s adapted his shots to still do the damage at the end.”

The stand-in Australia captain, George Bailey, admitted the absence of four key players for his side had made the difference.

Regular captain Michael Clarke, David Warner, Shane Watson and Brad Haddin were rested as Australia begin their preparations for their tour of South Africa next month.

“It does make a difference. [But] there’s some huge series coming up especially that Test series in South Africa,” Bailey said. “I don’t think any players have an issue that those guys had earned a rest.”